CCSS.Math.Content.HSN-VM.B.4c
The Standard
Understand vector subtraction v - w as v + (-w), where -w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students subtract vectors by changing the second vector to its opposite and adding corresponding components. They also show the difference on a diagram by connecting the vectors’ tips in the correct direction.
What Mastery Looks Like
- Students correctly reverse w, add components, and simplify signs. With common tails, they draw v - w from the tip of w to the tip of v and show that both methods agree.
Common Misconceptions
- Students may subtract magnitudes instead of corresponding components. They may reverse the wrong vector or draw the result from the tip of v to the tip of w. Negative components also cause frequent sign errors.
How to Assess It
- Give v = ⟨4, -1⟩ and w = ⟨-2, 3⟩. Ask students to calculate v - w, sketch both vectors with a common tail, and label the difference vector.
Lesson moves
Ways to Teach It
Place two taped arrows from one point on grid paper, then connect their tips in the direction representing the requested difference.
Ask students to explain why subtracting a vector changes its direction but not its length.
Play Vector Difference Match by pairing component calculations with correct tip-to-tip diagrams.
Model two walking displacements on a coordinate map, then find the change needed to move from one endpoint to the other.
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Printable HSN-VM.B.4c Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSN-VM.B.4c, with an answer key for the teacher on its own page. No account needed.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSN-VM.A.1
Vector subtraction requires knowing vectors as directed quantities with magnitude, direction, segment representations, and notation for vectors and lengths.
- CCSS.Math.Content.HSN-VM.B.4a
Vector subtraction is defined as adding the opposite vector, so graphical and component-wise addition methods directly carry over.
- CCSS.Math.Content.7.NS.A.1c
Component-wise vector subtraction requires signed coordinate subtraction and the idea that subtracting means adding an additive inverse.
Keep exploring
Related Standards
- CCSS.Math.Content.HSN-VM.B.4
(+) Add and subtract vectors.
- CCSS.Math.Content.HSN-VM.B.5a
Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(...
- CCSS.Math.Content.HSN-VM.A.2
(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
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